In a finding sure to inflame the math wars, a team of neuroscientists has revealed the crucial role played by rote memorization in the growing brains of young math students.

Memorizing the answers to simple math problems, such as basic addition or the multiplication tables, marks a key shift in a child’s cognitive development, because it helps bridge the gap from counting on fingers to complex calculation, according to the new brain scanning research.

The progression from counting on fingers to simply remembering that, for example, six plus three equals nine, parallels physical changes in a child’s brain, in which the hippocampus, a key brain structure for memory, gradually takes over from the pre-frontal parietal cortex, an area of higher order reasoning.

In effect, as young math students memorize the basics, their brains reorganize to accommodate the greater demands of more complex math. It is a gradual process, like “overlapping waves,” the researchers write, but it clearly shows that, for the growing child’s brain, rote memorization is a key step along the way to efficient mathematical reasoning.

By tracking a group of young students over the course of a year, the authors show “that children learn to associate individual problems with the correct answers. Repeated problem solving during the early stages of arithmetic skill development also contributes to memory re-encoding and consolidation, thus resulting in enhanced hippocampal activity and ability to recall basic arithmetic facts… The maturation of problem-solving skills is characterized by a gradual decrease in the use of inefficient procedures such as counting and an increase in the use of memory-based strategies.”

As a scientific justification of rote learning, the study seems likely to further polarize the controversy over math teaching styles, in which arithmetical fundamentalists are squared off against the popular and progressive forces of “discovery-based” learning, in which students are encouraged to find their own ways to the right answer.

By illustrating the benefit of repetition and memory, and showing how it serves as a stepping stone to mature calculation, the research is likely to embolden the fundamentalists, who have only recently started to win back lost ground.

The tried and true methods of addition, subtraction, multiplication and division work just fine as they have for centuries

When school returns next month in Alberta, for example, the requirement for students to memorize the multiplication tables will be reinstated, following an awkward climb down by the province’s education ministry in March.

One critic of the government’s adoption of “discovery-based learning,” Ken Porteous, a retired engineering professor, put it bluntly: “There is nothing to discover. The tried and true methods of addition, subtraction, multiplication and division work just fine as they have for centuries. There is no benefit and in fact a huge downside to students being asked to discover other methods of performing these operations and picking the one which they like. This just leads to confusion which ultimately translates into frustration, a strong dislike for mathematics and a desire to drop out of any form of mathematics course at the earliest opportunity.”

The new research, reported by American and South Korean scientists in the journal Nature Neuroscience, illustrates the “overlapping waves” theory of childhood cognitive development, in which advances are not abrupt but rather gradual shifts between strategies.

The study involved 68 children aged 7 to 9, all right-handed and healthy. They were given single-digit addition problems, and asked to solve them in the easiest way they knew how. Their strategies — whether counting on fingers or recalling the answer from memory — were recorded both by the experimenter’s observation of finger use or lip movement, and by the student’s self report.

The problems were deliberately tough, or as tough as basic addition can be. For example, they were not asked to add one or zero, or to add the same number to itself. In some cases, the lower number came first, and in others, the reverse.

In the parallel brain-scanning experiments, similar equations were shown to children in the scanner, with either correct answers or false ones that were only off by one or two. The scans were repeated more than a year later.

At the start, the greater role of the prefrontal cortex “likely reflects high levels of working memory and executive processing needed for implementing counting strategies, especially at a stage when children are still learning to solve arithmetic problems,” according to lead author Shaozheng Qin of Stanford University School of Medicine.

The increasing activity of the hippocampus as time went on, however, “is consistent with its known role in learning and memory for encoding and retrieval of facts and events, and matches our observation of greater reliance on memory-based retrieval of addition facts” over the course of the year-long experiment.

“In particular, the hippocampal system appears to be critical for children’s learning of mathematics in ways that are not evident in adults who have mastered basic skills,” the authors write. It appears to play a “critical, time-limited, role” in fostering “the gradual establishment of long-lasting knowledge represented in the neocortex,” a brain area of higher order functions.

This process is “time-limited” because the hippocampus’s role seems to taper off once this knowledge has been “consolidated” elsewhere in the brain. This same process might also be reflected in other cognitive systems, such as the development of language, the authors suggest.